Breakdown of Fermi's Golden Rule in 1d systems at non-zero temperature
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| Format: | Preprint |
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2025
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| _version_ | 1866915421345546240 |
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| author | Young, Thomas LLoyd, Jerome von Keyserlingk, Curt |
| author_facet | Young, Thomas LLoyd, Jerome von Keyserlingk, Curt |
| contents | In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles. In the limit of weak interaction strengths ($Δ$), a naive application of Fermi's Golden Rule (FGR) predicts an $\mathcal{O}(Δ^{2})$ quasiparticle decay rate. However, for 1d fermions on the lattice at $T>0$, this calculation gives a divergent result and the scaling of the quasiparticle lifetime with interaction strength remains an open question. In this work we propose a solution to this question: combining numerical simulations using the recently introduced dissipation-assisted operator evolution (DAOE) method, with non-perturbative diagrammatic re-summations, we predict a logarithmic enhancement of the quasiparticle decay rate $τ^{-1} \sim Δ^{2} \log Δ^{-2}$. We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems, and even in some classical systems, provided the non-interacting limit has quasiparticles with a generic dispersion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Breakdown of Fermi's Golden Rule in 1d systems at non-zero temperature Young, Thomas LLoyd, Jerome von Keyserlingk, Curt Quantum Physics Quantum Gases Strongly Correlated Electrons In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles. In the limit of weak interaction strengths ($Δ$), a naive application of Fermi's Golden Rule (FGR) predicts an $\mathcal{O}(Δ^{2})$ quasiparticle decay rate. However, for 1d fermions on the lattice at $T>0$, this calculation gives a divergent result and the scaling of the quasiparticle lifetime with interaction strength remains an open question. In this work we propose a solution to this question: combining numerical simulations using the recently introduced dissipation-assisted operator evolution (DAOE) method, with non-perturbative diagrammatic re-summations, we predict a logarithmic enhancement of the quasiparticle decay rate $τ^{-1} \sim Δ^{2} \log Δ^{-2}$. We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems, and even in some classical systems, provided the non-interacting limit has quasiparticles with a generic dispersion. |
| title | Breakdown of Fermi's Golden Rule in 1d systems at non-zero temperature |
| topic | Quantum Physics Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.00254 |